David Cameron has confirmed he will consider beefing up the new bill to give Scotland greater tax and welfare powers after Nicola Sturgeon complained the draft legislation failed to meet pledges on extra welfare powers made in the Smith commission.

Speaking after his first post-election meeting with the first minister in Edinburgh on Friday morning the prime minister said he would look again at the welfare powers after putting the Smith commission bill in his first Queen’s speech later this month.

Scottish parties are annoyed the draft bill fails to implement the Smith agreement proposal for Holyrood to introduce its own benefits or top up existing benefits.

On Thursday, Holyrood’s devolution bill committee said the UK’s draft legislation failed to live up to the “the spirit or substance” of Smith. Cameron said he could add extra powers going beyond Smith, which allows Scotland nearly full control over income tax, air passenger duty and housing benefit.

“I don’t rule out making sensible changes if sensible changes can be made,” he said, and promised to hold regular meetings with Sturgeon.

Asked about claims by a senior SNP source, disclosed by the Guardian, that the Scottish government could defy Cameron’s refusal to allow a second independence referendum by staging an unofficial vote without legal approval, Cameron suggested that source was Alex Salmond, the former SNP leader.

“I tend to take at face value what Alex Salmond says on the record rather than off the record. On the record he said it was a once-in-a-generation, potentially once-in-a-lifetime opportunity, and I’m sticking with that,” the prime minister said. Sturgeon described the meeting as constructive and business-like.

“Two things of significance were agreed in the meeting,” she said. First, there was a commitment from the prime minister that the legislation they will shortly introduce to the Westminster parliament to implement the proposals of the Smith commission will implement those proposals in full.

“We had a report from the Scottish parliament committee that said where we are thus far doesn’t fulfil the Smith commission proposals so there’s a commitment to do that and we’ll work with them to make sure that happens.

“Secondly, we will put forward proposals for devolution further than the commission proposals. The prime minister says they will consider those proposals. I’m not going to put words into his mouth and say he’s agreed any specific proposals.”