Boris Johnson said there was "no reason at all" to stop the vaccine's rollout and Scottish First Minister Nicola Sturgeon said she would accept her jab "without hesitation" when called on.
Northern Ireland's chief medical officer Dr Michael McBride also urged people to retain confidence in the jab as he received his first dose of the AstraZeneca version on Monday.
It comes as Germany, France, Spain and Italy paused injections of the vaccine amid concerns about blood clots in people who have had the shot, although the European Union's medical regulator insisted its benefits outweighed the risk of side effects.
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The Netherlands, the Republic of Ireland, Denmark, Norway, Bulgaria, Iceland and Thailand have already temporarily suspended their use of the jab.
The European Medicines Agency (EMA) said "many thousands of people" develop blood clots every year in the EU and "the number of thromboembolic events overall in vaccinated people seems not to be higher than that seen in the general population".
The EMA's safety committee is reviewing the data and working closely with the company, experts in blood disorders, and authorities including the UK's Medicines and Healthcare products Regulatory Agency (MHRA).
The committee will further review the information on Tuesday ahead of an extraordinary meeting on Thursday to consider any further action that may be needed.
Mr Johnson said the MRHA was "one of toughest and most experienced regulators in the world".
"They see no reason at all to discontinue the vaccination programme... for either of the vaccines that we're currently using," he said.
Speaking at a coronavirus briefing in Edinburgh on Monday, Ms Sturgeon said there was "no current evidence" linking the inoculation to blood clots.
"As soon as I get that invitation to go to be vaccinated, I will be there without hesitation, regardless of which of the vaccines I have been offered, and I would urge anybody who is getting the invitation to come and be vaccinated to get vaccinated," she said.
Ms Sturgeon is due to announce further aims for the easing of lockdown measures on hospitality and retail in Scotland on Tuesday.
Stormont ministers will meet on Tuesday to discuss easing lockdown restrictions.
Decisions are expected to focus on schooling and allowing more outdoor activities for young people.
Official data up to March 14 shows that of the 26,063,501 jabs of all types given in the UK so far, 24,453,221 were first doses - a rise of 257,010 on the previous day.
Some 1,610,280 were second doses, an increase of 25,371.
It comes as Wales marks the anniversary of the first confirmed death of a person in the country from Covid-19.
Two woodlands will be created in memory of those who have died from coronavirus during the pandemic and act as a "symbol of resilience", First Minister Mark Drakeford said.
The locations in north and south Wales will be designed to act as a permanent memorial "where families and others can come to remember all those we have lost".