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David Cameron has said he is "very happy" with assurances he has been given by Lady Warsi about her conduct following recent allegations.

The Tory co-chairman failed to declare she and a relative had stakes in the same firm before travelling together to Pakistan on a government trip in 2010.

Lady Warsi has apologised and the prime minister has referred the matter to his adviser on the ministerial code.

But the PM said he believed the probe was a matter of tying up "loose ends".

However, one Conservative MP has said Lady Warsi should stand down pending the investigation by Sir Alex Allan, No 10's adviser on ministerial interests, into whether she broke the ministerial code.

The ministerial code requires ministers to ensure no real or perceived conflict between their official responsibilities and their personal interests.

Lady Warsi, who sits in the cabinet as minister without portfolio, said it was "widely known" - both in her private office and the British High Commission in Pakistan - that Abid Hussain was her husband's second cousin.

Spice firm

But she said she did not realise the fact they had "a common business interest" as minority shareholders in a small food company, Rupert's Recipes, also had to be declared.

In a letter to Lady Warsi on Monday, Mr Cameron told her that she should have "pro-actively" informed the Foreign Office and the Cabinet Office that she and Mr Hussain were both shareholders in the company.

But he said it was important that Lady Warsi had declared her interest in the company to the Cabinet Office, that the trip to Pakistan was not trade-related and that Mr Hussain did not gain any business advantage from his involvement in voluntarily assisting the High Commission with the event.

Asked about Lady Warsi's future on Tuesday, Mr Cameron said he was "very happy with the explanation she has given".

"She has apologised for the mistake she has made," he told Sky News. "But I think it right for Sir Alex Allan just to see if there are any loose ends that need to be picked up. It's no more than that."

Conservative MP Nadine Dorries said that although Lady Warsi was "probably completely innocent", she believed she should step aside while the investigation takes place. "When she is found innocent David Cameron should provide his full support and reinstate her," she told the Financial Times.

'Pretty minor'

Fellow Conservative MP Louise Mensch told ����ý Radio 5Live that the prime minister had little option but to refer the matter to his adviser since Lady Warsi had herself admitted she had made a mistake in not declaring the business connection.

But she added: "As both the prime minister and Lady Warsi said in their letters, the breach is really pretty minor based on the fact that the guy did not go out at taxpayers' expense and did not receive any financial benefit from the trip.

"It does seem like an oversight and... I don't think that the special adviser is going to come down particularly hard on Lady Warsi as there was no advantage to her cousin from this trip."

Justice Secretary Ken Clarke said the media had subjected cabinet ministers to a "lynch mob", describing some allegations levelled against Lady Warsi as "downright silly".

"There is a bit of a fashion at the moment, the media do tend to act as a bit of a pack and they are steadily working through my colleagues trying to find things to complain about," he said.

"Sayeeda [Warsi], I am astonished by some of the complaints against her. It really is pedantic, some of it."

����ý political correspondent Iain Watson said Lady Warsi had her detractors in the party but her supporters were likely to argue that she was new in the job at the time of the trip and the ministerial code was not sufficiently explicit on what should and should not be declared.

The Conservative peer is already being investigated by a parliamentary standards watchdog over reports that she claimed accommodation allowance while staying with a friend rent-free.

Labour have questioned why Mr Cameron has referred Lady Warsi's conduct to his adviser on ministerial interests while he has declined to do the same for Culture Secretary Jeremy Hunt over his controversial handling of the BSkyB takeover bid.

But Mr Cameron said the cases were "very different", adding that: "In the case of Jeremy Hunt, obviously all of that has been gone through by the Leveson Inquiry."