Top Republican Party officials are escalating their fight with the Secret Service over the party’s convention in Milwaukee in July, demanding that the agency expand the security perimeter of the event so that protesters can be moved farther away from the arena where the main events will be held.

A cadre of senior GOP officials had a lengthy argument with Secret Service officials in Milwaukee on Thursday afternoon, according to three people familiar with the matter who spoke on the condition of anonymity to describe a private meeting. The Republicans repeatedly pushed the agency to widen the perimeter so that a prominent city park about a quarter-mile from the arena could not be used by the city for a designated protest zone. The Republicans also again demanded a meeting with the head of the Secret Service to no avail, the people familiar with the meeting said.