Cameron's letter to Klaus "firmly restates our current public position" on the European Union's reform treaty, a spokeswoman for Cameron said on Wednesday.
Klaus and Cameron, both Eurosceptics, could yet stand in the way of the Lisbon Treaty's ratification just when it appears close to becoming reality after years of argument and setbacks.
Any Czech or British veto would anger major EU states such as France or Germany, which have invested tremendous political capital in getting the treaty approved.
The pro-Conservative Daily Mail newspaper presented Cameron's letter as a "last-ditch attempt to scupper the controversial new EU treaty".
Cameron had reassured Klaus that if he held up the treaty, Cameron would stage a referendum in Britain if he wins power in an election due by next May, the newspaper said on its website.
It quoted a Conservative source as saying, "Cameron has told Klaus that if he can hold out for a few months, he'll be right there with him".
The Conservatives declined to release a copy of the letter and could not say when it was sent.
With the centre-right Conservatives about 17 points ahead of the ruling Labour Party in the opinion polls, the party is a strong favourite to win the next election.
The British parliament ratified the Lisbon Treaty after the Labour government rejected Conservative calls for a referendum.
The Conservatives say they will reverse Britain's ratification if voters reject it in their planned poll.
Only a handful of EU members have yet to ratify the Lisbon Treaty, designed to speed up decision-making in the 27-member union.
Irish voters, who rejected the charter last year, are due to vote a second time on 2 October.
The Czech upper and lower houses of parliament have approved the treaty. But ratification must be completed by Klaus, who has said he will not sign until all other EU countries have ratified it.
Klaus expressed confidence in New York on Tuesday that Irish voters would reject the treaty.
Britain's Conservatives have recently broken away from the main centre-right grouping in the European Parliament to form a new anti-federalist group with Czech and other politicians.
(EurActiv with Reuters.)