If it is asking for a payment method then you have no option but to enter one such as a credit or debit card. Read the support article Add a payment method to your Apple Account - Apple Support about how to do that.
For a more detailed response about what Apple actually says:
Apple's official support articles present multiple statements* about situations requiring the presence of a payment method at times, even for free items. You do not always have to have one, but if you are encountering one of those situations then you have no option but to enter a valid payment method if you wish to continue your purchase. The payment method may not be charged if you also have account balance or the item is free, but the payment method has to be present. You might even be able to remove it again immediately once Apple has seen it.
This next article lists valid payment methods for different countries but note that in this situation Apple Account balance alone apparently may not meet the requirement and you need to use another payment method until you find one that satisfies Apple's requirement (often a credit or debit card): Payment methods that you can use with your Apple Account - Apple Support .
If you have already entered a payment method, use the “Add a payment method” link above to check it. If a message appears in red there is a problem with it. If the information is still correct and current, contact your financial institution. Also check this resource --> If your payment method is declined in the App Store or iTunes Store - Apple Support
A previous post has come confusing statements:
Nowhere does Apple say that you have to have a payment method from the same country. In fact Apple has for many years avoided making a clear and simple statement saying that, which to me suggests it is a more complicated situation. All that Apple says in Change your Apple Account country or region - Apple Support about payment methods when changing country is: "Make sure that you have a payment method for your new country or region." It says "for", not "from". It then refers you to Payment methods that you can use with your Apple Account - Apple Support This may be to simply check if the payment method you used in your old country is also a payment type valid in your new country. Some payment types may be valid in one country but not in others. It does not say anything about your card having to be "from" the same country. This might just be poor wording on Apple's part in its documentation, but until they state clearly that the pay method must also be "from" the same country then I do not assume that it must be.
The only Apple statement I can find about international payment methods is what Apple says is in its support article: If your payment method is declined in the App Store or iTunes Store - Apple Support : "You might need to ask your financial institution to allow international purchases on your debit or credit card". If anything this is supporting the possible use of payment methods from other countries.
As for requirement #4 in another post, you do not necessarily have to be physically present in a country in order to use a payment method.