"I stand ready to work with my colleagues to support these measures with any additional Congressional action that may be necessary to ensure they are timely and effectively implemented," Cruz stated on Wednesday.
Cruz praised Trump for carrying through his campaign promises and delivering in terms of policies the American people "have waited far too long for action."
Earlier in the day, Trump signed executive orders to begin building a wall along the US southern border with Mexico and strengthening the implementation of US immigration law.
The president said in a press conference on Wednesday the wall will stop illegal immigrants from pouring into the United States and will disrupt the activities of drug cartels. Safe borders and economic cooperation will enhance US-Mexican relations to a degree not seen before and save lives, Trump added.