Walkouts also mooted at the Royal Mail after the recent rail strikes.
Tobias Ellwood claimed Russia will be "enjoying the self-inflicted distraction" from the war in Ukraine.
The Labour leader's authority is being challenged by frontbenchers after he ordered them not to stand on picket lines.
Boris Johnson warned the public they will have to "stay the course" as a wave of further strikes looms.
The party leader had warned his top team they had to show "leadership" by not joining pro-strike demonstrations.
A shadow cabinet member told HuffPost UK: "It’s a sensible decision given Tories want to blame us for their failings. We mustn’t fall into their trap."
Workers will be striking on Tuesday, Thursday and Saturday this week but protests could last much longer.
Simon Clarke acknowledged that the walkout would be a "huge inconvenience" – but refused to intervene.
The latest move comes after two days of strike action, on September 9 and 10, over a dispute about pay.
Pilots have walked out for two days, in the first strike to ever hit the airline. More than 1,700 flights have been cancelled.