Filed by Nuveen Municipal Trust (Commission File No. 333-239099)

pursuant to Rule 425 under the Securities Act of 1933, as amended,

and deemed filed pursuant to Rule 14a-6 under the Securities Exchange Act of 1934, as amended

Subject Company:

Nuveen Multistate Trust III (Commission File No. 811-07943)

Good day,

Attached is the proxy statement and information about the upcoming Nuveen Tennessee Municipal Bond Fund shareholder meeting.

Every vote is important and helps the fund reach the vote requirement for the meeting which is scheduled for Thursday, September 10, 2020. The Board is recommending a vote in favor of the proposal, which is described in detail in the attached proxy statement.

We would be happy to assist by answering any questions about the proposal and by recording a vote over the phone. Voting by phone is a quick way to participate and helps the Nuveen Tennessee Municipal Bond Fund avoid an adjournment.

Please call toll-free 1-866-704-4430 and provide reference number <<GS Number>>. We are available from 9:00am until 11:00pm Eastern Time weekdays and from Noon to 6:00pm Eastern Time on Saturday.

Thank you for your time and attention to this matter. We look forward to your call.

Best regards,

Supervisor

<<GS Number>>

Computershare

1-866-704-4430

211 Quality Circle, Ste. 210

College Station, TX 77845

www.cfs.computershare.com

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