LONDON—Britain plans to participate in a U.S.-led effort to train Syrian opposition troops, according to people familiar with the matter, but it will stop short of joining its closest ally in conducting airstrikes against Islamic State in Syria.

The U.K. government will announce in the coming days its role in training moderate Syrian opposition forces in neighboring countries with the aim of bolstering their ability to fight the extremist group, the people said. Turkey and Jordan will be involved in the plan, one of the people said.

The expected announcement marks an escalation of Britain’s involvement in the international effort against Islamic State after its moves to join airstrikes against the militant group in Iraq and carry out aerial surveillance missions over Syria. Some British politicians, though, say the U.K.’s military response hasn’t gone far enough and that Islamic State, also known as ISIS or ISIL, can only be defeated by tackling the extremists with airstrikes in Syria as well as Iraq.

Prime Minister David Cameron has repeatedly vowed to destroy the militant group, arguing that it poses a threat to security in Britain. Adding to the pressure on him to respond are the beheadings of two kidnapped Britons by Islamic State, which is believed to be holding at least one other British man captive.

But public opinion in the U.K. is divided over whether the British military should join the U.S. in bombing in Syria, especially after the loss of British soldiers’ lives in campaigns in Iraq and Afghanistan. Mr. Cameron suffered an embarrassing parliamentary defeat on the issue in 2013 when he sought to secure parliament’s backing for launching airstrikes in Syria in response to claims that Syrian President Bashar al-Assad used chemical weapons.