Rhun ap Iorwerth says he will "call out" the Labour UK government, if it fails to "do the right thing for Wales", and "take the fight" to the prime minister.
Speaking on BBC Politics Wales after Plaid Cymru won 43 seats in the Senedd election to become the largest party, he said the UK government had two choices.
"They can punish Wales for the way that we voted in this election, or they can reflect and say our indifference has been found out," he said.
UK government Secretary of State for Wales, Jo Stevens, said "our position has always been if it will benefit and make people's lives better in Wales then of course we will do things".
The Welsh nationalist party promised to "stand up for Wales" during the election campaign and ap Iorwerth is almost certainly going to become the party's first first minister in the coming days.
He said he hoped that the conversation between him, the UK government and Stevens "will be able to happen as soon as possible".
His demands for further devolution, he said, "could be brought together in a new Wales bill for Westminster".
The legislation, which could be brought forward by a Plaid Cymru MP, would be "dealing with fair funding, that HS2 unfairness, looking at police and crime and justice, looking at those elements of control over natural resources that we need to move forward".
Ap Iorwerth added: "It was Labour members and Labour policy in some areas, but they were unwilling to take the fight to the UK government.
"Well, this first minister is willing to take that fight to the UK government."
But Stevens suggested public services were the priority for the people of Wales, not transferring powers from Wales to Westminster.
"Nobody talked to me about it - I can honestly say to you that nobody raised it with me," she said.
In the past Jo Stevens has been accused by some within her own Labour party of being "anti-devolution".
Reform has 34 MSs, Labour just nine, the Conservatives seven, the Green Party two and one Liberal Democrat, in an expanded 96-member Welsh Parliament.
The result marked the end of Labour's century-long run of election success in Wales and 27 years of leading Welsh governments.
The path appears clear for ap Iorwerth to become first minister, something he hopes can happen as early as a vote on Tuesday.
The two Green Party MSs have said they will back him, the one Liberal Democrat Jane Dodds has said she will abstain and Labour interim Welsh leader, Ken Skates, indicated its group is unlikely to oppose him.
That means that even a combined vote of Reform and the Conservatives MSs could not block the Plaid leader from becoming first minister.
Outgoing First Minister Eluned Morgan lost her seat in the election, announcing she was resigning as Welsh Labour leader.
Ap Iorwerth also said he wants Plaid Cymru to govern on its own, rather than seeking to bring another party or parties into his administration.
He added he was seeking cross-party cooperation and wanted support from across the Senedd, and had spoken to all the other party leaders apart from Reform's Dan Thomas who "didn't feel like he wanted to speak with me as leader of Plaid Cymru".
That was denied by Reform.
"We provided a number for the purpose of Rhun contacting Dan," a spokesperson said.
"We made a clear communication channel if they wanted to reach him, he hasn't.
"Rhun said Dan didn't want to speak to him. That's not true."
Reform's version of events was rejected by Plaid.
Its spokesperson said: "Plaid Cymru approaches politics in a mature way and made contact with a senior member of Dan Thomas's team to arrange a courtesy call, as is customary between party leaders after an election.
"We were told explicitly that Dan Thomas would not be available and that any correspondence should be via his member of staff."
Skates, Senedd member for Fflint Wrecsam, revealed Labour Senedd members will hold a meeting on Monday to formally decide how to vote on Rhun ap Iorwerth's nomination for first minister.
"We're going to meet tomorrow to make a final decision on this, but the idea of teaming up with Reform is deeply unpleasant for all of the members of my group," he said.
Jane Dodds, the only Liberal Democrat member of the new parliament, said she would not stand in ap Iorwerth's way.
Speaking on her way to be sworn in as MS for Brycheiniog Tawe Nedd, she said: "I am really clear we are not going to back any Reform UK first minster.
"I am going to abstain if it's Rhun's name that goes forward.
"We don't support independence and Plaid don't have a majority so I will be abstaining."
But Green Party leader Anthony Slaughter said backing ap Iorwerth as the next first minister of Wales was a "no brainer".
"It's a no-brainer. Plaid has such a clear mandate to be the next first minister.
"Reform are nowhere close thankfully, so he has our support completely.
"We need to send a clear message that it is time for progressive politics in Wales.
"We will work with Rhun and Plaid on those issues."
It is the first time the Green Party has been represented in the Senedd.
"It's a historic moment, the Greens are in the Senedd and that will make such a difference," he added.
Ex-Conservative Senedd leader Paul Davies also confirmed he would like to be the new Llywydd, or speaker of the Senedd.
Skates described Labour's emphatic rejection by voters as "a catastrophic defeat, no doubt about it", calling Morgan a "phenomenal leader" in "difficult times".
He warned Welsh Labour to avoid the "blame game" and unite.
"We need to look at the reasons for our defeat in the most objective manner possibly," he said, saying he wanted the investigation to be like a "forensic study".
Later he announced he wanted to become the permanent Welsh Labour leader.
"I'd love the job for as long as it takes to build us back and to renew us and to return us to power, and it's my intention to do that in as short a period as possible."
Skates has held cabinet roles that have included the transport and economy portfolios.
On Sunday with Laura Kuenssberg, ap Iorwerth confirmed he had spoken to the SNP and Sinn Fein first ministers, in Scotland and Northern Ireland and believed they could all "work and stand together" to get a better deal for their populations.
"There are a number of different ways that we can work together," he said.
"The way that we use the natural resources off our coasts, for example.
"But there's a deeper sense than that, too, of being able to make a stand together to call for less inequality within these islands.
"We are a union that is not a union of equals, and the stronger we can stand together to make the case to the UK government for a new approach to dealing with Wales, Scotland and Northern Ireland [the better].
"We'll do that separately, I'll do it as first minister of Wales.
"My loyalty will always be to the people of Wales, but together there is strength too."
Ap Iowerth denied that his party's election triumph was simply down to Labour's unpopularity and many voters' desire to block Reform, arguing last Thursday also saw a "massive positive" for Plaid.
"Plaid Cymru has won a larger popular vote in this election than any other party in the history of devolution, that cannot all be put down to what is happening around the other political parties.
"It is about what we say in our determination to stand up for Wales in our programme.
"But of course, yes, people were turning to us to stop the populist right from getting a foothold and to be that voice for Wales that Labour showed they weren't able to [provide]."
Reform's Blaenau Gwent Caerffili Rhymni MS Llŷr Powell, runner-up to Plaid Cymru in last October's Caerphilly by-election, said his party intended to "add a higher level of scrutiny" to Cardiff Bay proceedings.
"We really need to make sure we get into the detail of what this new government will do.
"The budget will be a priority for us to make sure money goes where it needs to."
On the question of whether Reform would work with Plaid Cymru, he promised the approach would not be "tribal".
"We'll vote on issues which are important for the people of Wales and what they've given us a mandate to do, based on our manifesto.
"I'm not going to be tribal, I've been elected by the people of my constituency and they expect me to do the job.
"That's what I'm going to do."
Additional reporting by David Deans and Nelli Bird
