Rail strikes have caused travel disruption yet again this week, with national rail services impacted on Thursday and Saturday – and London Underground services hit on Friday.
But Mr Shapps told GB News' Breakfast with Anne and Mark that union bosses like the RMT's Mick Lynch "need to put the deal that's on the table, which is an eight percent pay rise over two years and no compulsory redundancies, to their membership".
He added that workers "may accept it" and stop strike action as he pinned the blame on high-earning union bosses.
It comes as London is hit with travel disruption.
Transport Secretary Grant Shapps GB News
Services on the vast majority of Tube lines are suspended, with a very limited operation elsewhere, according to Transport for London’s (TfL) website.
This has led to severe traffic jams as people use road transport to try to complete their journeys.
RMT union members are taking industrial action over issues including jobs and pensions.
There is also disruption to bus services in west and south-west London and parts of Surrey due to a strike on Friday and Saturday by drivers who are members of the Unite union.
Mainline train services started later than normal on Friday due to the knock-on effect of Thursday’s RMT strike at Network Rail and train operators across the country.
Just 70 percent of services will run during Friday as a whole. A further walkout on Saturday will reduce service levels to 20 percent.
Grant Shapps appeared on Breakfast with Anne and Mark GB News
RMT general secretary Mick Lynch claimed London Underground workers’ pensions are at risk
Speaking at a picket line in Acton, west London, he said: “We’re out on strike today because we haven’t got an agreement from the TfL LUL (London Underground Limited) about the future of the pension scheme, which is under threat and, at the moment, there’s negotiations going on between the Government, the Treasury, and Mayor (Sadiq) Khan’s office about the future funding of London Underground.
“They’ve cut £2billion from the funding and that has put at risk our members’ pensions.
“They want to decimate the pensions and change it into an entirely different, cheaper scheme, which will make all our members poorer in retirement and probably pay more while they are working.
“We haven’t gotten an agreement. There’s also threats to terms and conditions. We wanted a promise that terms and conditions won’t be diluted and there is a threat of a loss of jobs in certain sections of the Underground.”
He said he is “very sorry” that people are being inconvenienced by the strikes but defended the action, adding that the union has to show it is “deadly serious” about the livelihoods of its members.
Nick Dent, TfL’s director of customer operations, said it is “a difficult day” for travel in the capital, and “we’re advising customers not to travel on the Tube at all”.
London Mayor Sadiq Khan said: “The only reason for the strikes in recent weeks in London is because of the conditions the Government is trying to attach to a funding deal, and the trade unions are concerned about the consequences of those conditions on their members.
“This is about pension concerns that trade unions have. “I don’t want these conditions imposed on our transport workers.”
Figures from location technology firm TomTom show a sharp rise in road congestion in the city on Friday.
At 9am, the congestion level was 40 percent, compared with 26 percent at the same time last week.
The figures represent the proportion of additional time required for journeys compared with free-flow conditions.