AMMAN, Aug 31 (Reuters) - Syrian elite forces aided by pro-Iranian militias stepped up an offensive on Tuesday against a rebel enclave in a southwestern pocket bordering Jordan and Israel, according to residents, military and opposition sources. Fighting escalated earlier this week after the collapse of a Russian peace plan meant to avert an all-out offensive against Deraa al-Balaad, the core of the city of Deraa that has defied state authority since surrounding Deraa province was recaptured by President Bashar al-Assad"s forces in 2018. Witnesses and military sources said dozens of improvised missiles were fired into Deraa al-Balaad by the Syrian military"s pro-Iranian Fourth Division, which is backed by Iranian-financed local militias. A halt to fighting was announced after Russian generals offered a new plan that appeared to meet some of the rebel demands to involve the Russian military police in patrolling the enclave while allowing for the first time a Syrian army security presence in the stronghold. Rebels said they accepted the plan while the army said it would give its response by Wednesday to the deal that also allows the Syrian and Russian flags to be raised in the opposition bastion but gives Moscow"s guarantees that Iranian-backed army units cannot act with impunity. Army sources said Iranian-backed troops that have encircled the urban rebel enclave for the last two months and which brought forward reinforcements on Monday would be withdrawn under the deal. Deraa al-Balaad was the birthplace of peaceful protests against autocratic Assad family rule that broke out a decade ago - part of the pro-democracy Arab Spring uprisings - before spreading in response to deadly crackdowns by security forces and morphing into a devastating civil war. The latest army campaign came amid a spate of attacks over the past 24 hours by remnants of rebel groups on army checkpoints and outposts in Dael, Jasem and other towns across Deraa province, opposition sources and residents said. A Western intelligence source said several thousand families in towns caught in the crossfire had fled to safer areas near the Jordanian border where the Jordanian army was on alert for a possible new wave of refugees. The Syrian army said at least four soldiers were killed in ambushes on troops in the towns of Sanameen and Nawa, and that rebel shelling had caused several casualties in residential areas. Government forces, aided by Russian air power and Iranian militias, retook Deraa province in 2018, and Moscow assured Israel and the United States at the time that it would prevent Iranian-backed militias from encroaching on the border zone. That deal forced thousands of Western-backed rebels to hand over heavy weapons but kept Assad"s forces from entering Deraa al Balaad, whose administration remained in opposition hands. Pro-Assad forces have prevented food, medical and fuel supplies from reaching Deraa al-Balaad but have opened a corridor for civilians to leave, according to local officials and residents. The United States and its allies have voiced concern about Assad"s military campaign in Deraa, which they say is challenging Russia"s pledge to maintain stability and rein in Iran-backed militias hostile to Israel.