Home Office minister Lord Henley said the security of the UK border “remains our top priority” and contingency plans were in place.
He said extra staff had started training in April.
Meanwhile Labour MP John McDonnell has called for Heathrow to be shut on Wednesday on safety grounds.
Lord Henley, answering an urgent question in the House of Lords, said: “We are satisfied that security will be maintained.
“We started training additional staff in contingency in April and adequate resources are now available. Any staff deployed on the front line will have received training required to operate effectively.
“Arriving passengers will remain subject to checks at the border by appropriately trained staff.”
Hayes and Harlington MP Mr McDonnell, whose constituency includes Heathrow, said it was clear large numbers of staff at the London airport would be joining the strike.
Although attempts had been made to bring in extra people, it still meant that safety and security would be “in the hands of workers who are untrained in airport security or, at most, have had an inadequate couple of days’ training,” Mr McDonnell said.
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Nobody wants the public caught up in this, least of all this union. This is not something that we have done lightly”
Immigration Services Union
“I believe that if the government cannot settle this dispute in the next 24 hours the airport should be closed to ensure the safety and security of all those travelling and working at Heathrow,” he added.
Earlier the BBC learned that marines from Somerset’s 40 Commando had been put on standby to work at Heathrow during the strike and then stood down.
But a Ministry of Defence spokesman later said: “Border security is a matter for the Home Office which has said it is looking at a range of options to minimise disruption of the planned industrial action.
“No service personnel have been put on notice or standby to fulfil any role in relation to the planned industrial action by UKBA staff.”
The UK Border Agency said it was exploring options to reduce disruption.
A spokesman said: “The security of the UK border remains our top priority and it is absolutely right we explore all options to ensure we minimise any disruption caused by planned union action.”
Heathrow operator BAA has warned of possible “gridlock” on Wednesday and said passengers could face potential 12-hour delays getting through immigration at Heathrow.
The warning from Heathrow, which handles more international passengers than any other airport, came after immigration staff voted to join the strike by public sector workers.
Strikes are being held over changes to public sector pensions and thousands of border agency workers are expected to be among up to two million who could walk out.
Lucy Morton, deputy general secretary of the Immigration Services Union, said she regretted its members were striking.
She said: “Nobody wants the public caught up in this, least of all this union. This is not something that we have done lightly.”
She said the union members had been left “feeling there is nowhere else to go” and this was the only way “to make government listen to the people on the front line”.
The Immigration Services Union had never before taken industrial action she said.