Uri Blau reports (26 March 2017): 
The ministry spends tens of millions of shekels on cooperative efforts with the Histadrut labor federation, the Jewish Agency and various nongovernmental organizations in training representatives of the “true pluralistic face” of Israel in various forums.
The Strategic Affairs Ministry was established mainly as a consolation prize for ministers when the need arose to pad them with a semi-security portfolio during the formation of governing coalitions, and has taken on various forms. It was founded in 2006 as a portfolio tailored to Avigdor Lieberman. It was dismantled two years later and reestablished in 2009 in a different format. Under each ministry it was given new meaning and content.
During Lieberman’s tenure, its authority was defined mainly as “thwarting the Iranian nuclear program.” In addition, Nativ, which maintained contact with Jews in Eastern Europe during the Cold War and encouraged aliyah, came under its aegis. Then, under Moshe Ya’alon (2009-2013), the ministry focused on “Palestinian incitement” as well as the Iranian threat. During the term of Yuval Steinitz (2013-2015), the ministry was unified with the Intelligence Affairs Ministry into the “Intelligence Ministry.” In May 2015, it was once again separated out and given to gilad Erdan, incorporating the Public Diplomacy Ministry, which had been removed from the Prime Minister’s Office.
A harsh state comptroller’s report in 2016 concerning the “diplomatic-media struggle against the boycott movement and manifestations of anti-Semitism abroad,” noted that the transfer of authority to fight BDS from the Foreign Ministry to the Strategic Affairs Ministry was damaging to the powers of the Foreign Ministry and created unnecessary duplication that paralyzed government action in that area, as Barak Ravid reported extensively at the time.
According to the comptroller, after years of contention and mutual entrenchment, Prime Minister Benjamin Netanyahu had given in to pressure and shifted more powers for fighting BDS from the Foreign Ministry to the Strategic Affairs Ministry, together with major funding.
In October 2015, the security cabinet finally gave the Strategic Affairs Ministry responsibility to “guide, coordinate and integrate the activities of all the ministers and the government and of civil entities in Israel and abroad on the subject of the struggle against attempts to delegitimize Israel and the boycott movement.”
Nevertheless, tensions with the Foreign Ministry remained. The reason for this might also be a difference in approach. According to the comptroller’s report, the Foreign Ministry’s strategy of action against BDS “focuses on expanding dialogue with individuals, bodies, organizations, corporations and institutions abroad” – i.e., dialogue – as opposed to surveillance and more aggressive public diplomacy activities by the Strategic Affairs Ministry.
Others say the powers were moved from the Foreign Ministry to the Strategic Affairs Ministry due to what Netanyahu perceived as the too-liberal tendencies of the Foreign Ministry.The Strategic Affairs Ministry’s current director general, Sima Vaknin-Gil, was appointed in late 2015. In a meeting last August of the Knesset Special Committee for the Transparency and Accessibility of Government Information, Vaknin-Gil was asked what she defined as “winning” the battle against BDS. Winning, she said, meant that the “narrative in the world won’t be that Israel equals apartheid.” She explained that the ministry was training some 200 people, “among the best people in Israel,” as its ambassadors abroad.
This article, dated 16 May 2017, says:
Last year, it was reported that the ministry recruited personnel to head a "smear campaign" division in charge of collecting information on "organizations and those who lead de-legitimization in order to create counter-de-legitimization… including directly and through non-governmental entities."