That would depend on whether he is acting on the instructions of the President or if he's gone off on his own and making policy on his own.
On 1 Apr 1861, Seward wrote to Lincoln that they should abandon Ft. Sumter. Lincoln replied that same day staing that he did not "propose to abandon Fort Sumpter." In reference to foreign relations, the President wrote, 'Either the President must do it himself, and be all the while active in it, or devolve it on some member of his cabinet.' (Collected Works Of Lincoln, Roy P. Basler, ed., Vol. IV, pp.317-318.)
On 18 Apr 1861, The Daily Delta (New Orleans) editorialized:
It was to him [Justice Campbell], a Judge of the highest tribunal of the Government of the United States, that Lincoln and Seward gave the most positive assurances of peaceful purposes and of his determination not to reinforce the forts. This assurance was given as late as the 8th of April, after the orders had been sent from the War Department to fit out the naval expedition and move the troops southward to reinforce Sumter and Pickens.
They also write that Senator William Gwin of California, and congressmen Nelson and Etheridge of Tennessee received the same assurances. Regarding responsibility of Lincoln, I'll allow this statesman address the issue himself:
The absurdity of any such attempt to disassociate the action of the President from that of his Secretary, and to relieve the former of responsibility for the conduct of the latter, is too evident to require argument or comment. It is impossible to believe that, during this whole period of nearly a month, Mr. Lincoln was ignorant of the communications that were passing between the Confederate Commissioners and Mr. Seward, through the distinguished member of the Supreme Court -- still holding his seat as such -- who was acting as intermediary. On one occasion, Judge Campbell informs us that the Secretary, in the midst of an important interview, excused himself for the purpose of conferring with the President before giving a final answer, and left his visitor for some time, awaiting his return from that conference, when the answer was given, avowedly and directly proceeding from the President.
... No disavowal of his [Seward's] action, no apology nor explanation, was ever made. Politically and legally, the President is unquestionably responsible in all cases for the action of any member of his Cabinet, and in this case it is as preposterous to attempt to dissever from him the moral, as it would be impossible to relieve him of the legal, responsibility that rests upon the Government of the United States for the systematic series of frauds perpetrated by its authority.
Jefferson Davis, Rise and Fall of the Confederate Government, New York: D. Appleton & Co., 1881, Vol I, pp. 275-276.
What did some of the founding fathers say about executive reponsibility? Mr. Ames opined, "the officers: they will be stimulated to do their duty to the satisfaction of the principal [the President], who is to be responsible for the whole executive department."
Mr. Lee stated, "[t]he executive is the source of all appointments ... it will be his fault if any wicked or mischievous act is committed."