Despite warnings from Moscow not to do so, both Sweden and Finland are debating whether to apply to NATO, whose members are covered by its Article 5 mutual defense guarantee.

But Mr. Johnson’s pact would provide support to the Swedes and Finns during any accession process to NATO, when they could be particularly vulnerable to Russian retaliation, or if they decided not to join the club.

Mr. Johnson, visiting the two nations on Wednesday, was asked whether the agreement could mean deploying British troops to Finland, which has an 800-mile border with Russia.

“In the event of a disaster or in the event of an attack on either of us then, yes, we will come to each other’s assistance, including with military assistance,” he said. The type of help would depend on the request made, he added.

Sweden and Finland have offered mutual guarantees to Britain in return. “We will stand together and support each other in any circumstances in good and bad weather,” said the Finnish president, Sauli Niinisto, who added that his country’s decision to consider NATO membership had been prompted by Russia’s invasion of Ukraine.

Earlier, in Stockholm, after posing for a photo in a rowing boat with his Swedish counterpart, Magdalena Andersson, Mr. Johnson said that the agreement with Sweden “enshrines the values” held dear by both countries.

He added, “As you put it so well, Magdalena, when we were out on the lake: We are now literally and metaphorically in the same boat.”

For Mr. Johnson, who has struck up a close relationship with the Ukrainian president, Volodymyr Zelensky, the initiative is a helpful distraction from his political troubles at home after he was fined by the police for a lockdown breach in Downing Street. Asked on Wednesday whether that could prompt him to resign, Mr. Johnson deflected, saying he was more focused on the threat from Russia.

Wednesday’s move was also in line with Mr. Johnson’s efforts to forge a new foreign policy role for Britain after Brexit. Now outside the European Union and unable to influence its decisions, Britain is trying to make the most of its status, alongside France, as one of the nations in western Europe most willing and able to deploy significant military muscle.

In February, Britain announced a trilateral security pact with Ukraine and Poland, and British ministers have made several visits to Baltic States that feel particularly vulnerable to Russian aggression.

And Britain has played a leading role in discussions not only in NATO but in a less prominent diplomatic format, called the Joint Expeditionary Force, comprising Britain, Denmark, Estonia, Finland, Iceland, Latvia, Lithuania, the Netherlands, Norway and Sweden.

Some European Union diplomats believe that Britain could try to leverage that influence to divide the 27-nation bloc. For example, those member countries receiving military support or guarantees from Britain might be reluctant to take tough action against London in any escalation of its dispute with the European Union over post-Brexit trade arrangements for Northern Ireland.

But Downing Street, asked on Wednesday whether such connections could be made in talks with Sweden and Finland, said that there was no conditionality attached to its security guarantee.