David Cameron has sought to shore up the faltering campaign against independence, saying that keeping Scotland within the United Kingdom gave both "more oomph" by making them both "stronger, safer, more secure and more successful".

The prime minister launched a detailed defence of his track record in delivering extra powers to the Scottish, Welsh and Northern Irish parliaments, but admitted that many voters doubted he would honour his promises to hand further political and economic powers to Scotland if it rejected independence in September.

In a rare press conference with the Scottish press, Cameron insisted he was a man of his word: "All the political parties have in different ways, at different times been saying that further devolution is on the table after a no vote. I think it's very important Scottish voters going to the polls hear that message. Because it's very important that if you want further devolution, the way to get it is a no vote."

Seeking to dismiss allegations he is a "day tripper" with a two-day tour of Scotland, Cameron arrived at a Territorial Army base in Glasgow on Thursday to meet reservists and full-time soldiers due to provide security at the 2014 Commonwealth games in Glasgow.

Meanwhile, reports emerged that private polling for the Cabinet Office had confirmed a rise in support for independence shown by newspaper polls.

Cameron cited his government's implementation of new income tax and borrowing powers from 2016, new lawmaking powers for Cardiff, the promise of a Welsh referendum on tax-raising, and devolution of policing to Northern Ireland.

A Tory party commission on further devolution – being run by a former Tory leader in the Lords, Lord Strathclyde, and due to report this month on its proposals for greater tax and legal powers – had done good work, Cameron said.

"I would say as prime minister over these last four years, I made some promises about further devolution to Scotland. I think some people might have doubted whether they're going to be fulfilled but they've absolutely been fulfilled," Cameron said.

"I think I have a track record of showing respect for the nations of the United Kingdom and achieving devolution so that our family of nations can stay together and find a settlement which we all are comfortable with."

He added: "Of course Scotland can have some of those things if it was independent, but think of what we have together. Think of how more oomph we have."

Cameron said he had full confidence in Alistair Darling, the chairman of Better Together, after reports that the former Labour chancellor had been sidelined in the campaign because of disappointment at his leadership.

Cameron said: "I think that Better Together are doing a very good job. I think they're bringing together an incredibly diverse range of politicians, who all share the same vision that we're better off together as a united kingdom."

But he failed to mention Darling by name, implying he does have reservations about the Better Together chairman.

The prime minister twice referred to "very strong speeches" by Gordon Brown and recalled the memory of John Smith, the former Labour leader who died 20 years ago, during the briefing with reporters.

Citing Brown's speeches and the involvement of other Labour figures and the Liberal Democrats campaigning alongside the Tories, Cameron said he planned a series of visits to Scotland before the referendum.

"I'm keen to play my part. I'm confident in the campaign and confident in its success. We take nothing for granted so we will fight very, very hard right up until the last vote is counted."

Cameron also confirmed he had no plans to resign as prime minister if there was a yes vote in September. "My name is not on the ballot paper. I think we need to be very clear about this. My future will be decided in about 360 days when the country goes to the polls for a general election," he said. Alex Salmond, the first minister, reacted by saying Scottish voters had no faith in promises from Tory prime ministers, particularly as the party had only one MP in Scotland, and again pressed his demand for a head-to-head TV debate with Cameron.

"Nobody will believe Tory promises of more powers for Scotland, because the last time that happened the only thing Scotland got was Thatcherism and 18 years of Tory governments we didn't vote for," Salmond said.

"The prime minister is perfectly entitled to come to Scotland, and we are perfectly entitled to ask why he isn't prepared to have a debate in Scotland. He is prepared to have a debate with Ukip and the Greens, but not on the future of Scotland."