It is difficult to understand why Pharaoh wanted the frogs to be removed only on the following day. Although we know from Proverbs 21,10 that wicked people harbour a death wish (unconsciously), this applies only in the abstract. No wicked person deliberately opts for continued flagellation when given a chance to escape the pain involved. Why then did Pharaoh ask Moses to make his prayer effective only on the following day? At first glance one may be tempted to conclude that Pharaoh misinterpreted Moses' offer as proof of his awareness that the plague was about to come to an end, and that he wanted to take the credit for this by appearing to pray for the removal of the frogs at once. Pharaoh therefore wanted to show up Moses as a fraud. He interpreted Moses' use of the word התפאר as a trick designed to induce him to ask for the immediate removal of the frogs. This is why he decided to suffer a little longer if only he could expose Moses as a fraud.
What is wrong with this theory is that if Pharaoh wanted to unmask Moses as a fraud he did not really have to extend the period of his suffering at all by asking Moses not to pray until the following day. Besides, Pharaoh had never heard of a prayer that is offered up at one time and is not to be effective until the following day. This is why he wanted Moses to demonstrate that though he prayed now and his prayer would be accepted, the removal of the frogs would not be implemented until the morrow. This was the challenge Pharaoh presented to Moses when he said: למחר. He wanted proof that Moses prayed immediately though the frogs would not disappear until the morrow. When Moses told Pharaoh: כדברך, "as you said," he meant that he had accepted Pharaoh's challenge. Moses did not leave the city to offer his prayer (as he did on other occasions) but prayed inside the city in order for everyone to be aware precisely when he had prayed. This is why the Torah writes: "Moses and Aaron left the presence of Pharaoh and Moses cried out to God concerning the frogs God had brought on Pharaoh, etc." Moses prayed concerning two matters. 1) Removal of the frogs. 2) Not to remove the frogs until the following day. This is why the Torah states על דבר הצפרדעים, "concerning the matter of the frogs," instead of להסיר הצפרדעים, "to remove the frogs."