From the Eretz Hemdah website (link):
Q: Is it permitted to get married on Yom Ha’atzmaut and Yom Yerushalayim?
A: As you know, there is an ancient custom not to marry during the period of sefira, when we commemorate the death of the students of Rabbi Akiva. There are opinions that are lenient in a variety of cases of need and mitzva (see a survey of opinions in Yein Hatov II:11), but the minhag, in general, is kept strictly.
Chief Rabbi Nissim (ibid.) felt that celebrating the miracles and Divine blessings associated with Yom Ha’atzmaut (5 Iyar) is reason enough to allow a full suspension of the minhagim of sefira, including marriage, on that day. Other distinguished contemporaries of Rav Nissim, while appreciating, as he did, the importance of those crucial, historic events, believed that allowing marriages on Yom Ha’atzmaut was too revolutionary a leniency to adopt in our generation. See the responsa of Rav Ovadia Hadaya (Yaskil Avdi VI, 10) and Chief Rabbi Unterman (Shevet Miyehuda 60), who [adopt] the latter view.
After confirming with religious councils in Israel that the practice is to not allow marriages on Yom Ha’atzmaut, we feel that this custom should be followed, but those who decide to have the wedding then, have whom to rely on.
The situation on Yom Yerushalayim (28 Iyar) is different, as it falls after Lag Ba’omer. Since, according to the minhag of many, the restrictions of the sefira period are over (see Shulchan Aruch, Orach Chayim 493 and Mishna Berura, ad loc.), there is significantly more room for leniency. Consequently, the Chief Rabbinate Council (under the presidency of Chief Rabbis Unterman and Nissim, z.t.l.) issued a directive to allow marriages on Yom Yerushalayim. In Bemareh Habazak III, pg. 100 we cited this ruling and stressed its particular relevance for those who have not yet fulfilled the mitzva of pru u’revu.