RNA - Germany said it was in no hurry to send extra troops to the long-running conflict and Britain said it would not go beyond an uplift already promised earlier this year, Telegraph reported.
France said no decision had been taken, but one French military expert said he would be “astonished” if Paris agreed to go back to Afghanistan. Spain and Italy’s government’s both declined to comment.
Trump is expected to send up to 4,000 more US troops after on Monday night he abandoned calls for a swift withdrawal from the country and instead made an open-ended commitment to America’s longest ever war.
In an about face on a conflict he once called futile, Mr Trump said US troops would now “fight to win”.
"We are not nation-building again. We are killing terrorists," he said in a prime-time televised address at a military base outside Washington.
"The consequences of a rapid exit are both predictable and unacceptable," he said. "A hasty withdrawal would create a vacuum that terrorists, including ISIL and al Qaeda, would instantly fill."
The reinforcements to train and advise the struggling Afghan forces and hunt down the militants come on top of around 8,400 already deployed.
US commanders earlier this year warned they were at a stalemate and Jim Mattis, the Defence Secretary admitted America was “not winning”. A string of districts have since fallen to Taliban-led insurgents.
The president demanded Pakistan do more to tackle terrorist "safe havens".
"Pakistan has much to gain from partnering with our effort in Afghanistan. It has much to lose by continuing to harbour terrorists," he said.
And he warned the Afghan government that it should not view US support as a "blank check".
"America will work with the Afghan government as long as we see determination and progress," he said.
"However, our commitment is not unlimited, and our support is not a blank cheque. The American people expect to see real reforms and real results."
America’s Nato allies also had to do more, Mr Trump said.
He said: “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.”
European allies appeared to shy away from his request however.
The German defence minister said her country, which has 950 troops in Afghanistan, would not be among the first nations to contribute more.
Ursula von der Leyen said: "We increased our troop numbers by 18 percent last year when others were cutting theirs. So we don't see ourselves in the front row of people who should be asked for more soldiers."
The Ministry of Defence in London said it had already announced in June that 85 more soldiers would be sent, bringing the UK detachment to 600.
A Whitehall source said: “We don’t see that number changing”.
French defence expert Jean-Dominique Merchet, said: "I would be astonished if France was prepared to send troops back to Afghanistan.
"We are already heavily present in the Sahel with 4,500 troops in Mali, Niger, Chad and Burkina Faso, and in Iraq, where there are around 1,000 French soldiers. That's a lot.
"France lost not far off 100 men in Afghanistan for nothing and their presence there could not be called a success."
Mr Trump’s decision to remain in Afghanistan risked angering supporters who voted for his ‘America First’ campaign promises to end US foreign interventions.
Breitbart, the conservative news website run by his former strategist Steve Bannon, called the new strategy a "flip-flop."
After his speech, Mr Trump flew to Arizona to rally supporters and try to recapture the Republican fervour that helped put him in office.
The two-day trip, which also includes a stop in Reno, Nevada, on Wednesday to speak to veterans at an American Legion conference, marks his farthest journey west since taking office in January.
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