Shri Ram did not ask her to take Agnipariksha of Mata Sita but he provoked her for that because when she came to him after she was rescued, he was rude to her and it hurt her. She told Laxman to organise a pyre and when he looked at Shri Ram, he hinted him to do it and Laxman lit the pyre. When she entered it Agni Dev came and gave testimony of her purity. Then Shri Ram revealed that he didn't have any doubt on his wife, she was protected by her own moral power and Ravana couldn't touch her but the test was necessary so that vile people (Rakshasas and enemies of royal houses) couldn't use her abduction as an excuse to malign her name and the names of royal houses of Janaka and Raghu. Mata Sita also never blamed Shri Ram because she knew him more than anyone else. Shri Ram never wanted Mata Sita to take Agnipariksha, she herself took it.