World football's governing body added that there would not be another time slot for the team to train, but did not say whether Argentina's session, scheduled for 1130 local time (17:30 CET), would go ahead as planned.
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"The Spanish national team's training session on the pitches at the Melanie Lane Training Ground in New Jersey has been suspended in accordance with the US storm safety protocol," the Spanish federation (RFEF) said in a statement.
"The players are currently taking part in a warm-up session indoors."
The final will kick off at 15:00 local time (21:00 CET) on Sunday.