Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Situational Awareness; Communication Breakdown; Confusion
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Taxiway
Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification
Airport; Procedure
Pushed from [gate] and was told to contact ground at spot 5. Contacted ground and they said to taxi Alpha-Echo-Bravo to runway 4 and we were number 1 for departure; Once on Bravo taxiway; Ground told us to monitor Tower. Once on Tower Freq; the Captain taxied as advised by Ground instructions (crossing the ILS critical area). Tower then instructed us to stop before the critical area as we crossed the ILS Critical Area. I advised Tower that we were stopping at that point. No point did the ground controller tell us to stop before the critical area. Should be noted that today both times in LGA the ILS critical area was included in the ATIS. One time ground was advising to hold short during taxi instructions; the other time they weren't saying to hold short as the ATIS had mentioned and aircraft were crossing the ILS critical area with no issues.Due diligence should always be maintained both on the ground and in the air. Safety has been and always be my first focus while operating an aircraft. Missing the assignment of stopping short of the ILS critical area should have been a priority and questioned if there was doubt. The confusion is also compounded due to the fact before this flight I have heard ground stating to hold short of the ILS critical area. We operated to ZZZ and then returned to LGA. When we returned to LGA it was overheard the controllers to hold short of the ILS critical area. The following day the same message was in the ATIS and all aircraft in front of us were not stopping short of the area.  This is not said to be an excuse; but to point out when there is factors outside the flight deck that can start a crew down the wrong path of operation of the aircraft I should take even more precautions as a First Officer.
[Report narrative contained no additional information]
A flight crew reported inadvertently taxiing into an ILS critical area due to communication ambiguities with the taxi clearance issued by ATC.