Here are relevant quotes from the statement itself.
The executive branch shall construe sections 914 and 1512 of the Act, which purport to make consultation with specified Members of Congress a precondition to the execution of the law, as calling for but not mandating such consultation, as is consistent with the Constitution's provisions concerning the separate powers of the Congress to legislate and the President to execute the laws.
A number of provisions in the Act call for the executive branch to furnish information to the Congress or other entities on various subjects. These provisions include sections 219, 313, 360, 1211, 1212, 1213, 1227, 1402, and 3116 of the Act, section 427 of title 10, United States Code, as amended by section 932 of the Act, and section 1093 of the Ronald W. Reagan National Defense Authorization Act for Fiscal Year 2005 (Public Law 108-375) as amended by section 1061 of the Act. The executive branch shall construe such provisions in a manner consistent with the President's constitutional authority to withhold information the disclosure of which could impair foreign relations, the national security, the deliberative processes of the Executive, or the performance of the Executive's constitutional duties.
The executive branch shall construe as advisory section 1011(b)(2) of the Act, which purports to prohibit the Secretary of the Navy from retiring a specified warship from operational status unless, among other things, a treaty organization established by the U.S. and foreign nations gives formal notice that it does not desire to maintain and operate that warship. If construed as mandatory rather than advisory, the provision would impermissibly interfere with the President's constitutional authority to conduct the Nation's foreign affairs and as Commander in Chief.
The executive branch shall construe section 1211, which purports to require the executive branch to undertake certain consultations with foreign governments and follow certain steps in formulating and executing U.S. foreign policy, in a manner consistent with the President's constitutional authorities to conduct the Nation's foreign affairs and to supervise the unitary executive branch.
As is consistent with the principle of statutory construction of giving effect to each of two statutes addressing the same subject whenever they can co-exist, the executive branch shall construe section 130d of title 10, as amended by section 1405 of the Act, which provides further protection against disclosure of certain homeland security information in certain circumstances, as in addition to, and not in derogation of, the broader protection against disclosure of information afforded by section 892 of the Homeland Security Act of 2002 and other law protecting broadly against disclosure of such information.
Note that the text attempts to define certain presidential powers as off limits to congressional limitations. These would be the inherent powers the president claims during times of crisis, like the current war on terror. The question remains, because the Supreme Court has yet to rule on any of this, whether it within the president's authority to define what the inherent powers are and to refuse to carry out a law based on his interpretation of it.