The home secretary says he will keep the number of Border Force vessels under close review, as migrants continue to cross the English Channel from France.
But Sajid Javid has not pledged to provide any more boats, saying he wants to ensure Britain does not "encourage more people to make this dangerous journey", adding that there was "no one easy answer".
He is expected to speak to the French interior minister on Sunday, Sky News understands.
Mr Javid, who cut short a family holiday to help deal with what he has described as a "major incident", is facing calls from MPs to send in the Royal Navy.
In a statement released on Saturday evening, he said the situation in the Channel was of "grave concern, with people gambling their lives in reckless attempts to reach the UK in unsafe boats and treacherous conditions".
He added, however, that it was "vital we strike a balance between protecting them and protecting our borders".
Regarding resources, he said: "I continue to keep the number of Border Force cutters in the Channel under close review, but there is no one easy answer to this complex problem."
He continued: "We have been working closely with our domestic partners and the French for some time to address this issue.
"I will continue to work closely with all partners to ensure we do even more to intercept these boats before they reach the UK, to tackle the organised crime gangs that facilitate many of these dangerous journeys, and to deter and protect those driven to make them."
Earlier, the National Crime Agency said dozens of attempts by migrants to cross the Channel from France had been disrupted in the last three weeks.
However, Chris Hogben, the head of an NCA-led organised immigration crime task force, said more crossing attempts were likely.
Mr Hogben said French colleagues had "disrupted numerous attempts, recovering at least 95 migrants including nine children, and arrested seven people caught attempting to facilitate these crossings".
"Dozens of attempted crossings have already been prevented," he added.
Three "suspected facilitators" have also been arrested and charged in France, he said. They will face trial in the new year.
Mr Hogben added that the "organised criminals behind these most recent attempts are in the main not UK-based, but through our close collaboration with French authorities we are still having an impact on them and their activity".
Two separate groups of migrants attempting to enter the UK by boat were picked up on Friday, totalling 12 people.
Some of them are being treated for hypothermia.
Mr Javid has come under increasing pressure to provide more resources in the Channel.
Dover MP Charlie Elphicke called for cutters to be brought back from search-and-rescue operations in the Mediterranean.
He said he did not accept they would be "anything other than a deterrent", dismissing suggestions that patrol boats might act as a magnet for migrants hoping to be picked up and brought to the UK.
"Everyone knows that the rescues are being done by the RNLI, who are volunteers and going out over the Christmas period making sure people are not at harm on the high seas," he said.
Independent MP and home affairs committee member John Woodcock told The Sun: "The public is losing confidence in the struggling Border Force. It's time to stop the rot by sending in the Royal Navy.
"If the civilian force can't cope, the navy must stop this crisis becoming a catastrophe."
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And another committee member, Conservative MP Tim Loughton, told the newspaper: "There is a serious security implication, as this is a likely route undesirables who have been fighting in Syria will use if they want to return to the UK.
"Of course there is now a case for the Royal Navy to be brought in to do border protection in the Channel."