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Boris Johnson says there is "still time" for Russia to "step back" from the situation with Ukraine, urging all sides to carry on talking.
Tension is continuing to grow on the border between the countries, where Russia has more than 100,000 troops.
No 10 said Mr Johnson would hold a Cobra meeting on Tuesday to discuss the UK's response to the pressures.
Labour leader Sir Keir Starmer said he supported the government, but wanted to introduce tougher sanctions on Russia.
He also said Parliament should be recalled if an invasion took place, adding: "We must have a swift and strong response, a united response from the United Kingdom."
Russia has long been opposed to the former Soviet republic of Ukraine growing closer to Europe and its institutions.
President Vladimir Putin has demanded a guarantee from the West that Ukraine will not join Nato - a defensive alliance of 30 countries.
But Nato has said it will not close down any future agreement with Ukraine.
While the diplomatic row has played out, Russia has amassed 100,000 troops along Ukraine's border, with reports that a further 30,000 are engaged in military exercises in Belarus.
Russia insists it is not planning to invade Ukraine, but European countries - including the UK - and the US have been providing support, such as training and weapons, and numerous governments have told their citizens to leave the country.
'Still time'
Speaking to reporters on a visit to Scotland, Mr Johnson said the situation was "very, very dangerous and difficult", adding: "We are on the edge of a precipice".
But he said there was "still time for President Putin to step back".
The PM added: "What we are urging is for everybody to engage in dialogue, for a conversation to take place and for the Russians to avoid what I think everybody, certainly everybody in the UK, would consider to be a disastrous mistake."
Mr Johnson has cut short planned visits in the north of England to return to London for security briefings.
Foreign Secretary Liz Truss is holding an emergency Cobra meeting on Monday afternoon, and the PM will hold another on Tuesday.
Meanwhile, Labour's leader has given his backing to the government.
On a visit to Sunderland, Sir Keir told reporters: "Russia wants to see our allies divided, it wants to see division in the United Kingdom.
"And we are not going to divide and, therefore, we support the government in what it's doing."
But he did urge the PM to "go further" with sanctions in response to "Russian aggression".
The government has introduced new powers to "broaden the range" of Russian people and businesses the UK could target with sanctions.
But MPs criticised a lack of debate in the Commons on the plans, as Parliament is now on recess.