Wudu is not required for السعي between الصفا and المروةh عند the consensus of scholars from all four schools of jurisprudence. Unlike الطواف, where the requirement of الوضوء is debated, scholars unanimously agree that السعي is valid without الوضوء. This is a significant practical relief for الحجاج, especially during the extreme crowding and الحرارة of الحج season when maintaining ablution is very difficult.
The evidence for this ruling is clear. النبي (صلى الله عليه وسلم) told Aisha when she was menstruating: 'Do everything the الحجاج do, but do not perform الطواف around the House.' This hadith explicitly permitted her to perform السعي (and all other rites) while in a state of menstruation, which is a greater state of ritual impurity than minor hadath. If السعي is valid without the major purification (الغسل) required after menstruation, it is certainly valid without the minor purification (الوضوء).
الشيخ ابن باز and الشيخ ابن عثيمين both confirmed that while performing السعي with الوضوء is better and more rewarding — as الوضوء is مستحب for all acts of worship — it is not a condition of validity. A الحاج who breaks الوضوء during السعي may continue without renewing it. The اللجنة الدائمة issued the same ruling, emphasizing that this is a matter of scholarly agreement (ijma') and there is no significant dispute on this point.