RAQQA, Syria (Reuters) - U.S.-backed militias expect to push all Islamic State fighters out of their former Syrian headquarters of Raqqa in less than a month, a Kurdish commander told Reuters on Monday.  Under the banner of the Syrian Democratic Forces (SDF), the militias have hemmed the jihadists into a few districts in the north of the city. The Kurdish and Arab militias pushed into the city in June after fighting for months to encircle it with the help of U.S.-led jets and special forces.  As the noose tightens, the reaction of Daesh gets fiercer,  said Jihan Sheikh Ahmed, spokeswoman for the Raqqa offensive, using the Arabic acronym for Islamic State.  In the coming days, the battles will be at their most intense...   We expect, under our plan, that we will be able to liberate Raqqa in less than a month.  Islamic State has lost much of its territory in Syria this year under separate offensives by the SDF and the Russia-backed Syrian military. Its fighters have fallen back to its last major footholds, the cities and towns in the fertile strip along the Euphrates river downstream of Raqqa. The SDF said last week that, after seizing 80 percent of Raqqa, the battle for the city had entered its final stages.  With the Kurdish YPG militia at its forefront, the SDF has closed in from three directions. Islamic State militants put up tough resistance, planting scores of mines around their districts, Ahmed said.  SDF forces sought to  meet up from several axes  to squeeze the Islamic State enclave, said a field commander in the northeast of Raqqa. Shefkar Hemo said his fighters had faced fewer mortar shells and car bombs recently, with the jihadists relying more heavily on snipers.   The breach of enemy lines is clear on the ground... Daesh are hiding behind civilians,  he said.  Another field commander in the city said the latest phase of the battle had proved difficult. SDF officials estimate that 700-1,000 Islamic State fighters are holed up in a pocket in the city. Ahmed said she did not expect them to surrender and the SDF would never allow them passage out.  Thousands of civilians remain trapped there too, and Ahmed accused Islamic State snipers of targeting them.    Daesh is also entrenched in the National Hospital, which they consider a main position,  she said.  Our forces besieged the hospital,  but were being cautious to avoid damaging it, she said. Earlier this month, Physicians for Human Rights said that poorly-equipped hospital was the last medical facility operating in the city.  The New York-based group said intense bombing by the U.S.-led coalition had hit civilian facilities. The coalition says it is careful to avoid civilian casualties during bombing runs in Syria and neighboring Iraq.  The  caliphate  that Islamic State declared in 2014, spanning both countries, lost its de-facto Iraqi capital of Mosul in July when Iraqi forces took the city.  