Dear refuge of my weary soul

When God said that he would consume Israel in his wrath, Moses prayed and God “repented”.  When the people of Ninevah turned from their evil, God “repented” of the judgment he foretold through Jonah (much to Jonah’s dismay). Does prayer still work the same way today? Can we change the mind of God through prayer? More importantly, did these people in the Old Testament really cause God to “repent”?