David Cameron said he wanted to govern with respect
Prime Minister David Cameron has called for a "fresh start" in relations between the Scots and UK governments, as he met First Minister Alex Salmond.
During a visit to Holyrood, Mr Cameron said he was open to a request from the SNP administration for a £700m package to boost the economy.
But he warned the UK spending deficit had to be tackled.
Mr Cameron also called for an "agenda of respect" between the Westminster and Edinburgh parliaments.
Mr Salmond welcomed Mr Cameron's comments, but said they must be backed with "concrete action".
Brian Taylor Political editor
David Cameron said this was his first visit as prime minister to a parliament anywhere. He has yet to go to Westminster.
His talks with the opposition leaders were held in Queensberry House, where the second Duke of that ilk crafted and propagated the Union Treaty in 1707.
And the PM had to enter Holyrood via a side door because of a noisy protest outside against public sector cuts.
Alex Salmond said after the talks that he had been surprised that the new PM was ready to engage, seriously, about financial issues such as new borrowing powers or Scotland's demand for a comparable share of the money currently being spent in the east end of London in association with the Olympics.
As the prime minister spoke inside the parliament, a group of protesters gathered outside to campaign against spending cuts and questioning the Tories' mandate to govern Scotland, after the party returned only one Scottish MP at last week's general election.
But Mr Cameron, who was accompanied by Scottish Secretary Danny Alexander, a Lib Dem MP, said the contest had been "a UK election and a UK result".
The prime minister, who also met Holyrood opposition leaders, said: "I want a real agenda of respect between our parliaments.
"I want to see Scottish ministers able to appear in front of select committees in Westminster and I believe that, if the Scottish Parliament would wish it, I would appear every year at the Scottish Parliament to answer questions."
Mr Cameron added: "This agenda is about parliaments working together, of governing with respect, both because I believe Scotland deserves that respect and because I want to try and win Scotland's respect as the prime minister of the United Kingdom."
On government relations, he said: "I also want to see a fresh start in the relationship between the British prime minister and the Scottish first minister.
"This relationship is important - however much we disagree about issues, we should try to work together for the benefit of the whole of the United Kingdom and for the benefit of Scotland as well. That is what I'm determined to do."
Alex Salmond was "impressed by the prime minister's awareness of the issues"
Turning his attention to the SNP government's planned independence referendum, the prime minister added: "We will have our arguments - I will never give ground on my commitment to the United Kingdom and keeping our United Kingdom together, but it's a relationship I want to try to make work well."
Mr Salmond called on the Tory-Lib Dem coalition government to bring forward £350m of capital spending to aid Scotland's economic recovery, and also argued Scotland was owed £165m over five years in "consequential" funding, as a result of public spending in relation to the London Olympics.
The SNP leader also requested the Treasury released cash for Scotland held in the fossil fuel levy, worth £180m, and will press the case to give enhanced borrowing powers to Holyrood, as recommended by the Calman Commission review of devolution.
Mr Salmond, said: "I think it's a good thing that the prime minister fulfilled his commitment to come to the Scottish Parliament and to meet the Scottish government, with the secretary of State for Scotland, in the first week in office.
"But, as I've said before the meeting and I'll say again now, a respect agenda has to be carried forward in deeds and actions.
"I'm certain the prime minister, as we all are, will be judged by your deeds, and therefore what I would articulate is I'd like to see that respect agenda, which I welcome, to be carried forward into concrete action."
Scottish Labour leader Iain Gray said Mr Cameron must recognise Labour as the "voice of Scotland" if he was sincere about a new spirit of co-operation.
"David Cameron's visit should not be just a photo-opportunity," said Mr Gray, adding: "He knows the Tories were overwhelmingly rejected by the Scottish electorate as were the SNP.
"I told him there is widespread fear his plans to cut £6bn will throw the economy back into recession, and that Scotland wanted him to drop those plans.
Later, Mr Cameron met soldiers of the Black Watch on a visit to Fort George at Ardersier, near Inverness, which is in Mr Alexander's Inverness, Nairn, Badenoch and Strathspey constituency.
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