The pair became friendly last year when Williams performed on The X Factor and then returned to duet with Murs in the show's final.
Speaking to Celebritain, the 'Please Don't Let Me Go' singer admitted that he had decided not to send Williams and new wife Ayda Field a present.
"I sent a good luck email," he said. "I wouldn't send a present because there's nothing that he hasn't got!"
He added: "I sent a message saying congratulations. She's a lovely lady, I've met her and she's great so I'm really happy for him. He was really happy and emailed me straight back and said he was so happy, and so happy to be with her."
Both Murs and Williams will appear in Blackpool next month, for the switching on of the 2010 Illuminations.
"I can't wait to do that at the end of September," Murs said. "It will be great to catch up with Rob about how he is and how he's doing since the wedding."
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