UK Prime Minister David Cameron's spokesperson refused to say whether the government still had confidence in Rifkind, who also heads the UK parliament's intelligence and security committee.
Rifkind and Straw were approached by Channel 4 and Telegraph reporters, who posed as agents from a non-existent Hong Kong-based communications agency PMR.
Both appeared willing to arrange meet-ups with their political contacts, while Rifkind claimed he could offer "useful access" to all British ambassadors around the world, according to Channel 4.
Straw was also suspended overnight after the video revealed him boasting about successfully operating "under the radar" on behalf of a commodity firm and being paid 60,000 pounds a year (over $92,000). He claimed to have used his influence to change EU laws to benefit the company, and also to have convinced the Ukrainian prime minister to change local laws for the same reason.
The politicians have denied any wrongdoing. Straw said he had offered his services to the fake Hong Kong firm as an experienced politician with ministerial background, and not as a member of parliament. He is to stand down after the next general election in May 2015.