The Public and Commercial Services union walk-out Thursday would have struck border controls at London Heathrow and other airports, The Independent reported.
The newspaper said the timing of the strike had been condemned by politicians, while the Home Office had said it was planning to seek a High Court injunction to stop it. For its part, the union said its members had been subjected to "disgraceful" attacks from government ministers since the announcement last week of the strike.
At issue was the planned cut of 8,500 jobs at the Home Office, including 1,000 from the border force, The Independent said.
The walk-out was suspended because the Home Office announced it was creating 800 new jobs, 300 in passport offices -- officials told the union about them Tuesday.
PCS leader Mark Serwotka said the announced new jobs proved the government has made mistakes in cutting thousands of jobs in recent years, The Independent said.