Air Carrier First Officer reported receiving an EGPWS warning and also from the ATC tower; that the aircraft was too low on the initial approach. The pilot crew immediately climbed back to a safe altitude.

Narrative

On a south heading if 180 we were cleared for a visual approach into Runway XX into ZZZ. We were receiving vectors and our last given vector was heading 180 to set us on a downwind about 7-10 miles from the runway. We were cleared pilots discretion to 3500 feet then once reaching the downwind leg ZZZ approach cleared us for the visual for Runway XX. The Pilot Flying (PF) then bugged 2500 feet in the altitude select to coincide with the final altitude at the FAF that they were referencing as back up to aid in the visual approach. As the crew continued the descent ZZZ Tower notified of us of a low altitude alert due to a tower in the area. Immediately the crew started to corrected course and reverse the descent into a climb. After starting the correction the crew got an aural message of 'pull up- pull up.' The crew continued the correction of the Enhanced Ground Proximity Warning System (EGPWS) caution via hand flying and eliminating all automation. (Crew disconnect the autopilot and cleared the flight once getting the alert from ZZZ Tower) The crew ascended about 300-500 feet and hand flew a left base which set up a stable approach to landing at ZZZ.Multiple factors caused the event to happen. It was a lack of awareness of the crew to see the obstacles and be aware of how the aircraft was vectored in the vicinity of the obstacles. It was also inattention to detail of the ZZZ surrounding area and how as towers were in sight; they also had towers offset. Another factor would be the large discrepancy between MSA and glide slope intercept altitude at the FAF. Make a section in the company 10-7 pages explaining and highlighting that a group of larger towers is in the direct downwind of Runway XX (left hand traffic) and that to safely avoid you must stay above the MSA to avoid conflict but staying at MSA altitude could leave the aircraft in an unstable state.