LONDON — Shocked by the deadliest terrorist attack on Britons in a decade, Prime Minister David Cameron promised a “full spectrum” response on Monday to the assault, which killed 39 tourists at a resort in Sousse, Tunisia, on Friday. At least 18 of the victims, and possibly as many as 30, were British.

Mr. Cameron sent security officials and government ministers to the scene and promised to step up the fight against extremism in Britain. Theresa May, the home secretary, and Tobias Ellwood, a Foreign Office minister, went on Monday to Tunisia, where British officials are working with the local authorities to assess security at beach resorts frequented by European tourists.

In concrete policy terms, however, Mr. Cameron’s reaction was cautious, and he did not promise any immediate new antiterrorism measures at home or any increase in Britain’s military involvement in fighting Islamic State militants.