POWER OF ATTORNEY

Know all by these presents:

        That the undersigned hereby constitutes and appoints each of Gerard
Michel, Sandra Pennell and David Hoffman signing individually, as the
undersigned's true and lawful attorneys-in-fact and agents to:

        (1) execute for and on behalf of the undersigned, in the undersigned's
            capacity as an officer, director and/or more than 10% stockholder
            of Delcath Systems, Inc. (the "Company"), Forms 3, 4, and 5 in
            accordance with Section 16(a) of the Securities Exchange Act of
            1934, as amended (the "Exchange Act") and the rules thereunder;

        (2) do and perform any and all acts for and on behalf of the
            undersigned which may be necessary or desirable to complete and
            execute any such Form 3, 4, or 5 (including any amendments
            thereto), and timely file such form with the SEC and any stock
            exchange or similar authority; and

        (3) take any other action of any type whatsoever in connection with the
            foregoing which, in the opinion of such attorney-in-fact, may be of
            benefit to, in the best interest of, or legally required by, the
            undersigned, it being understood that the documents executed by
            such attorney-in-fact on behalf of the undersigned pursuant to this
            power of Attorney shall be in such form and shall contain such
            terms and conditions as such attorney-in-fact may approve in such
            attorney-in-fact's discretion.

        The undersigned hereby grants to each attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might
or could do if personally present, with full power of substitution or
revocation, hereby ratifying and confirming all that such attorney-in-fact, or
such attorney-in-fact's substitute or substitutes, shall lawfully do or cause
to be done by virtue of this power of attorney and the rights and powers herein
granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to
comply with Section 16 of the Exchange Act.

        This Power of Attorney shall remain in full force and effect until the
earliest to occur of (a) the undersigned is no longer required to file Forms 3,
4 and 5 with respect to the undersigned's holdings of and transactions in
securities issued by the Company, (b) revocation by the undersigned in a signed
writing delivered to the foregoing attorneys-in-fact or (c) as to any attorney-
in-fact individually, until such attorney-in-fact is no longer employed by the
Company.

        In witness whereof, the undersigned has caused this Power of Attorney
to be executed as of June 22, 2023.

                                                      By: /s/ Vojislav Vukovic
                                                          --------------------

                                                      Name: Vojislav Vukovic
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