Mr Johnson will continue with diplomatic efforts this week despite Downing Street assessing that all information suggests Moscow could be planning an invasion “at any moment”.
He is understood to be receiving daily intelligence briefings from security chiefs on the increasing build-up of Russian forces, and will travel to Europe towards the end of the week.
Mr Johnson was also said to be working with allies to provide more defensive and economic support to Kiev, with an announcement expected for the coming days.
“The crisis on Ukraine’s border has reached a critical juncture," a Downing Street spokeswoman said.
"All the information we have suggests Russia could be planning an invasion of Ukraine at any moment. This would have disastrous consequences for both Ukraine and Russia.
“There is still a window of opportunity for de-escalation and diplomacy, and the prime minister will continue to work tirelessly alongside our allies to get Russia to step back from the brink.”
The crucial phase in trying to de-escalate Russian build-up on the border with Ukraine comes at a difficult time for Mr Johnson, with critics saying he is distracted by the police investigation centred on Downing Street.
He must answer this week a legal questionnaire sent to him by officers investigating claims of lockdown-breaching parties, which could ultimately see him being fined if he is found to have broken the law.
That outcome would inevitably lead to even more widespread calls for his resignation, and Tories pressuring for a vote of no confidence against Mr Johnson's leadership.
Downing Street did not set out which world leaders he was hoping to talk to this week or where he planned to travel.
But it was understood Mr Johnson is keen to engage with Nordic and Baltic countries.
UK Defence Secretary Ben Wallace will head to Brussels for a meeting of Nato defence ministers this week to discuss their response to the crisis.