after entering my payment method, asks to contact iTunes support. cannot download apps in app store

Then you should do as instructed and speak to Support to solve the issue.

World-wide Apple Support -

Contact Apple for support and service – Apple Support

M1 Mac mini, macOS 13.5.2;  Watch, series 7 GPS/cellular, watchOS 10.0.1; iPad Pro 2nd Gen, iPadOS 17.0.1; iPhone 12 Pro, iOS 17.0.1; TV 4th Gen, tvOS 17; HomePods, audioOS 17 and Airport Express w/ Airplay 2

Start here, please check ⤵️

1.

If you see a message that says "Your account has been disabled in the App Store and iTunes", there is a problem with your payment method on your account, to resolve the problem you need help from Apple support,  click -> contact Apple Support for help.

2.

If your Apple ID is locked or disabled -> If your Apple ID is locked or disabled - Apple Support (CA)

-> Get a verification code and sign in with two-factor authentication

Get a verification code and sign in with two-factor authentication - Apple Support

3.

See -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

• If you want to change your card, you need to add first the new card, then remove the old card.
• or if you use your Apple Account balance, you need to set your Apple Account balance as your default payment.

See also -> Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)

fyi: Not all credit & debit cards seem to work with App Store / iTunes Store, try a different one, or preferably a credit card. If your card is not accepted as a paymenf method, you need to contact your bank.

If you have followed all the steps and instructions and if you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.