Denials of entry for people at official crossings and border arrests reached 39,006 in November, up 12 percent from 34,855 in October and more than double the 15,766 who were stopped or arrested in April. But November's figure was still down 38 percent from 63,361 for November of 2016, shortly before Trump took office.
Border arrests don't capture how many people got away from agents but are widely used to understand trends in how many attempt to enter the country illegally.
Trump touted the dramatic decline in arrests during the early months of his presidency as evidence that his administration was making the border more secure. Reasons for the drop and recent rise are unclear but Trump's pledge to build a wall with Mexico may have initially discouraged people from trying and now be having less impact.
Administration officials said last week that they were concerned about an increase in families and unaccompanied children showing up at the U.S. border with Mexico. Customs and Border Protection asked for changes to a 2008 law that gave new protections to children entering the country who are not from Canada or Mexico and prevents them from quickly being sent home.