Defence Secretary Sir Michael Fallon has welcomed President Donald Trump's pledge to beef up the US military presence in Afghanistan, saying allies must "stay the course" in the conflict.
However, it is thought unlikely that the UK will increase its deployment to the country in the wake of Mr Trump's announcement.
Labour leader Jeremy Corbyn was critical of the US president, saying more troops and bombs will continue the failure of military action in Afghanistan.
In a dramatic turnaround from his election campaign calls for the 16-year war to be brought to an end, Mr Trump unveiled a new south Asia strategy designed to prevent a Taliban takeover, target Islamic State and al Qaida and stop mass terror attacks in the USA.
And he said he was "confident" that Nato allies - which include Britain - would hike troops and funding in line with the US.
But in a statement responding to the announcement, Sir Michael gave no indication that the UK is considering an increase to its 500-strong deployment, and stressed that an additional 85 troops were committed as recently as June.
Sir Michael was briefed by his US counterpart, Jim Mattis, ahead of the president's announcement, in the first of a series of phone calls to Nato allies.
But it is understood that London has received no formal request from the US for further military support, and UK sources played down the prospects of an increase in British boots on the ground.
Sir Michael said: "The US commitment is very welcome. In my call with Secretary Mattis yesterday we agreed that, despite the challenges, we have to stay the course in Afghanistan to help build up its fragile democracy and reduce the terrorist threat to the West.
"It's in all our interests that Afghanistan becomes more prosperous and safer: that's why we announced our own troop increase back in June."
Mr Trump made repeated calls ahead of his election for US troops to be withdrawn from Afghanistan, where they have been involved in military operations since the 2001 war to topple the Taliban following the 9/11 attacks.
But in an address to the nation from Fort Myer, near Washington DC, on Monday night, the president acknowledged that he had changed his mind on the issue and decided to go against his "original instinct".
Mr Corbyn said: "The war in Afghanistan has failed.
"After 16 years of bloodshed and destruction, the Taliban are undefeated and terrorism is no less of a threat at home. In fact, it has spread.
"The British Government should make clear to Donald Trump that his strategy of more bombing and a new troop surge will continue this failure, not obediently applaud his latest policy U-turn."
In a speech evoking the 9/11 events in 2001 which drew the US into the war, as well as the recent terror attack in Barcelona, Mr Trump said American policy would now focus not on nation-building but on killing terrorists.
His comments come after Pentagon officials proposed a 4,000-troop increase to the 8,400-strong US deployment in the country, to bolster the Kabul government, train Afghan forces and fight the Taliban and other militant groups.
"From now on, victory will have a clear definition: attacking our enemies, obliterating Isis, crushing al Qaida, preventing the Taliban from taking over Afghanistan and stopping mass terror attacks against America before they emerge," said Mr Trump.
"We will ask our Nato allies and global partners to support our new strategy with additional troop and funding increases in line with our own - we are confident they will."
Mr Trump's announcement was welcomed by Nato Secretary-General Jens Stoltenberg, who noted that recent weeks have seen more than 15 member states pledging additional contributions to its mission in the country, where the alliance currently has more than 12,000 troops deployed.
"I welcome President Trump's new, conditions-based approach to Afghanistan and the region," said Mr Stoltenberg.
"Nato remains fully committed to Afghanistan and I am looking forward to discussing the way ahead with Secretary Mattis and our allies and international partners."
Liberal Democrat foreign affairs spokeswoman and deputy leader Jo Swinson said: "For once, sense seems to have prevailed in the White House."
But she added: "The Government's rapid statement of support for Trump today contrasts with its failure to swiftly condemn his divisive views and actions in the past.
"Simply pouring more troops into Afghanistan will not work without a broader strategy involving careful diplomacy and redoubled efforts to build a stable government."
Then-president George W Bush sent troops into Afghanistan after the 9/11 attacks and his successor Barack Obama increased the military presence to more than 100,000 but failed to bring the war to a close as planned.
Britain provided the second largest contribution to Nato operations in Afghanistan following 9/11, with around 9,500 UK troops deployed in Helmand province alone at its peak.
British combat troops left Afghanistan in 2014, with a small contingent remaining on the ground to train local military forces.
A total of 456 British forces personnel and Ministry of Defence officials have died while serving in the country since the start of operations in October 2001.
General Joseph Votel, the top US commander for the Middle East, said the first new forces will be deployed to Afghanistan within days or weeks.
He told reporters fresh troops will arrive on the ground "pretty quickly", adding: "What's most important for us now is to get some capabilities in to have an impact on the current fighting season."