Short answer. Yes, if that motion is allowed under COMELEC's own procedural rules. Rule 64, Section 3 provides that filing such a motion interrupts the thirty-day period, and if the motion is denied, you get the remaining period, but never less than five days from notice of denial, to file your petition.
What the law says
The filing of a motion for new trial or reconsideration of said judgment or final order or resolution, if allowed under the procedural rules of the Commission concerned, shall interrupt the period herein fixed.
Rule 64, Section 3 — Time to file petition. Read the full provision →
The thirty-day deadline this rule sets
Rule 64, Section 3 fixes the window for challenging a COMELEC judgment, final order, or resolution before the Supreme Court: the petition shall be filed within thirty days from notice of the judgment or final order or resolution sought to be reviewed. That thirty-day period is the baseline you are working against, running from the notice you received of the ruling you want reviewed.
Why a motion for reconsideration can pause that clock
The rule then addresses exactly your situation: the filing of a motion for new trial or reconsideration of said judgment or final order or resolution, if allowed under the procedural rules of the Commission concerned, shall interrupt the period herein fixed. The key condition is that the motion has to be one COMELEC's own procedural rules actually allow; assuming it is, filing it stops the thirty-day clock rather than letting it keep running while COMELEC considers your motion.
What happens once the motion is decided
If COMELEC denies the motion, the rule tells you what remains of your window: the aggrieved party may file the petition within the remaining period, but which shall not be less than five days in any event, reckoned from notice of denial. So the clock resumes from where it stopped when you filed the motion, picking up whatever days were left of the original thirty, except that you are guaranteed at least five days from the notice of denial even if very little of the original period remained when you filed the motion.
Why checking COMELEC's own rules matters
Because the interruption only applies to a motion if allowed under the procedural rules of the Commission concerned, whether your particular motion for reconsideration actually pauses the clock depends on COMELEC's own procedure, not just on this rule alone. A motion that COMELEC's rules do not recognize as available in your type of proceeding would not necessarily get the benefit of this interruption, even though it was filed and labeled a motion for reconsideration. Confirming that the motion is one COMELEC's rules actually allow in your case is what determines whether Rule 64's interruption applies at all.