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Mortgage payments have nothing to do with your private family dealings. (I don't know why you think there could be a connection.) Of course you can invite your family members, at any time!

@sandey

For mortgage approval you might be asked about the number of dependent people in your household.

Once your mortgage is approved, the bank is not involved in your family affairs, as Beppi said. Nobody from the banks or credit institution will police your living circumstances, as long as you are paying the agreed mortgage installments (and your home needs to be insured - as per my knowledge).

@WilliamNZ

Thank you Beppi and William for clarifying my query. I have still one doubt, my question is rather on "invitation letter" than mortgage. Sending invitation letter you have to have some criteria, like bank statements and salary slips. So, if the Bundestage finds that my mortgage is running, will they reject the "initation letter" to invite my parents or in-laws?

To invite relatives or friends for a visit is totally independent of having a mortgage or not; neither for the mortgage giver or government officials. But if the intention is to have them immigrate then one should know that there is no chain migration in Germany. Foreigners with legal residency can usually bring their spouse and minor children on a family reunion visa. Parents, grandparents, aunts, uncles, cousins, sibling, adult children, grandkids, nieces and nephews… None of this matters. If, and this is a big if, one can really prove a hardship situation say a parent is old, destitute and living in country at war, or they have a medical situation not treatable in a underdeveloped county then they might be allowed but on the condition the family pay their expenses.  But just being alone for example doesn’t count. Just being poor doesn’t either because the family in Germany could send them money. And while poverty exists in India, it’s not like there are no adequate medical facilities, housing or food. It’s a matter of money.

    @WilliamNZ
Thank you Beppi and William for clarifying my query. I have still one doubt, my question is rather on "invitation letter" than mortgage. Sending invitation letter you have to have some criteria, like bank statements and salary slips. So, if the Bundestage finds that my mortgage is running, will they reject the "initation letter" to invite my parents or in-laws?
   

    -@sandey

I understand you mean the Verpflichtungserklärung = acting as a guarantor for a visa applicant, for example for a visitor visa. please correct me, if I am wrong.

As part of the process of obtaining the document that makes you responsible for a visa national visitor, you have to go to your local immigration office or another authority tasked with this, in Berlin it´s a special subdivision of teh police, it´s not the Bundestag that will decide.

You will have to bring proof of your household income, usually including bank statements. Your mortgage payments would take the place of your rent payments, so nothing unusual about having a mortgage (or not).

What´s important is that you can demonstrate that you have enough income to accommodate the number of people you are inviting and are not going to be destitute because of it.