I am planning to continue to pay the mortgage after immigration. But I don't know if the bank will allow me to pay house mortgage from another country.
You'll have to talk to your mortgage lender about that, I doubt there is a 'generic' answer to it. I do currently have a house in another country that I'm paying a mortgage on, but the lender wasn't too happy with that. They still did accept it, but the bigger problem for me is refinancing it as an investment property when you're not in the country.
Also, it probably depends on what your plans are - are you planning to go abroad for a few years, then return? Emigrate for good? Rent out the place while you're gone?
As I can attest to, even with a local agent a house 5000 miles away can be more of a pain in the posterior than you'd expect it to be.