President Trump issued a proclamation today continuing his earlier proclamation issued on April 22, 2020. This new proclamation goes into effect at 12.01 AM on June 24th and suspends and limits the entry of any individual seeking entry pursuant to any of the following nonimmigrant visas:
(a) an H-1B or H-2B visa, and any individual accompanying or following to join such individual;
(b) a J visa, to the extent the individual is participating in an intern, trainee, teacher, camp counselor, au pair, or summer work travel program, and any individual accompanying or following to join such individual; and
(c) an L visa, and any individual accompanying or following to join such individual.
The proclamation shall apply only to an individual who:
(i) is outside the United States on the effective date of this proclamation;
(ii) does not have a nonimmigrant visa that is valid on the effective date of this proclamation; and
(iii) does not have an official travel document other than a visa (such as a transportation letter, an appropriate boarding foil, or an advance parole document) that is valid on the effective date of this proclamation or issued on any date thereafter that permits him or her to travel to the United States and seek entry or admission.
As before, the suspension and limitation on entry shall not apply to:
(i) any lawful permanent resident of the United States;
(ii) any individual who is the spouse or child of a United States citizen;
(iii) any individual seeking to enter the United States to provide temporary labor or services essential to the United States food supply chain; and
(iv) any individual whose entry would be in the national interest as determined by the Secretary of State, the Secretary of Homeland Security, or their respective designees.
This Proclamation does NOT affect those individuals who are already in the US on H1B, L1 or J1 status. Those individuals whose entry was already suspended under the previous proclamation will continue to be suspended until December 31, 2020.

USCIS has announced that it will resume Premium Processing service in phases, as follows - 
1. June 1, 2020 - PP resumes for all eligible I140 cases.
2. June 8, 2020 - PP request can be made for all cap-exempt H-1B petitions (either because employer is cap-exempt or because beneficiary has previously been counted against the cap) and I-129 petitions for other visa categories that were filed before June 8, 2020 and are pending.
3. June 15, 2020 - PP request can be filed concurrently with H1B petitions which are cap-exempt due to the employer being a non-profit or other cap-exempt organization or due to the employee having a Conrad waiver.
4. June 22, 2020 - PP request can be made for all other I129 petitions, including H1B- cap subject petitions for FY 2021.