Repeating after the muezzin whilst doing wudoo’ and during Tawaaf
Question

                When a person is doing wudoo’, is it Sunnah for him to respond to the muezzin at that time or not?
Praise be to Allah. 
          Ibn Hajar al-Haythami was asked this question, and he 
          replied as follows: 
 
          When a person is doing wudoo’, he should respond, because 
          the Sunnah for the one who is doing wudoo’ is to refrain from speaking 
          apart from making dhikr (remembering Allaah). There is some dispute 
          as to whether making specific dhikr for each part of the body washed 
          is mandoob (recommended) or not, but the more correct view is that it 
          is not mandoob, as al-Nawawi said, because the ahaadeeth concerning 
          that are not free of lies and narrators who were accused of lying. (In 
          other words, the specific du’aa’s whilst washing the various parts of 
          the body during wudoo’ are not saheeh). 
 
          With regard to responding (to the muezzin), it is mandoob 
          according to scholarly consensus, hence they said that it is also mandoob 
          for one who is doing Tawaaf, even though he also has others dhikrs which 
          he should recite according to scholarly consensus, so that is more appropriate 
          in the case of the one who is doing wudoo’. 
 
          With regard to finishing wudoo’, if a person’s finishing 
          wudoo’ coincides with the muezzin’s finishing the adhaan, then he may 
          recite the dhikr of wudoo, as stated by al-Balqeeni in his fatwa, giving 
          it precedence over the dhikr to be recited immediately after the adhaan, 
          because the dhikr for wudoo’ has to do with the act of worship that 
          he has just completed, then he may recite the dhikr immediately following 
          the adhaan. 
 
          He said, it is good if he recites the Shahaadatayn of 
          wudoo’ then the du’aa’ following the adhaan, because it has to do with 
          praying for the Prophet 
          
          (peace and blessings of Allaah be upon him), then he may make du’aa’ 
          for himself.