Please complete this task on an urgent basis/urgently.

Please help. Thanks!

I started to respond to this yesterday and I got confused because I have difficulty stating this as a command — "Please complete..." — but the second sentence is better. It just doesn't sound natural to me.

It would be more common to see the idea expressed this way:

"It is urgent that this task be completed."

Look at these examples:

https://www.wordhippo.com/what-is/sentences-with-the-word/urgently.html

Maybe izzythepush or PUNKEY can give you a better answer.

I prefer the second as well, but I would not use either. I would say something like, “Please give this matter your immediate attention.”

Please urgently complete this task.

Please urgently complete this task.
Please complete this task urgently.

Do the sentences have the same meaning? Which one is better?

They have the same meaning but I prefer the first sentence.

https://ell.stackexchange.com/questions/8870/where-is-the-correct-place-to-place-adverbs-in-sentences