Well, you did post a very similar question in the past Database to find intron sequences? and you got a good number of answers for it. I would recommend reading through those and following the links that are specified there.

The short answer to your question is that you cannot directly download intronic sequences from NCBI. What you can do is post process the files that you get from NCBI and extract that information. If you want to know how to do that you should open a new specific question along the way: How to extract introns from a genbank file?

1. Generate intron bed as described here from the UCSC. (you can use refseq introns if required)
2. Download the reference genome.

3. Use nucBed from bedtools to get the fasta sequences:

   nucBed -s -fi Homo_sapiens.GRCh37.62.fa -bed hg19.introns.bed -seq | awk '(NR>1){print ">"$4 "| "$1":"$2"-"$3"\n" $16}' > hg19.introns.fasta

Output:

>uc001aaa.3_intron_0_0_1_12228_f| 1:12227-12612
GTAAGTAGTGCTTGTGCTCATCTCCTTGGCTGTGATACGTGGCCGGCCCTCGCTCCAGCAGCTGGACCCCTACCTGCCGTCTGCTGCCATCGGAGCCCAAAGCCGGGCTGTGACTGCTCAGACCAGCCGGCTGGAGGGAGGGGCTCAGCAGGTCTGGCTTTGGCCCTGGGAGAGCAGGTGGAAGATCAGGCAGGCCATCGCTGCCA
CAGAACCCAGTGGATTGGCCTAGGTGGGATCTCTGAGCTCAACAAGCCCTCTCTGGGTGGTAGGTGCAGAGACGGGAGGGGCAGAGCCGCAGGCACAGCCAAGAGGGCTGAAGAAATGGTAGAACGGAGCAGCTGGTGATGTGTGGGCCCACCGGCCCCAGGCTCCTGTCTCCCCCCAG
>uc001aaa.3_intron_1_0_1_12722_f| 1:12721-13220
GTGAGAGGAGAGTAGACAGTGAGTGGGAGTGGCGTCGCCCCTAGGGCTCTACGGGGCCGGCGTCTCCTGTCTCCTGGAGAGGCTTCGATGCCCCTCCACACCCTCTTGATCTTCCCTGTGATGTCATCTGGAGCCCTGCTGCTTGCGGTGGCCTATAAAGCCTCCTAGTCTGGCTCCAAGGCCTGGCAGAGTCTTTCCCAGGGAAA
GCTACAAGCAGCAAACAGTCTGCATGGGTCATCCCCTTCACTCCCAGCTCAGAGCCCAGGCCAGGGGCCCCCAAGAAAGGCTCTGGTGGAGAACCTGTGCATGAAGGCTGTCAACCAGTCCATAGGCAAGCCTGGCTGCCTCCAGCTGGGTCGACAGACAGGGGCTGGAGAAGGGGAGAAGAGGAAAGTGAGGTTGCCTGCCCTGT
CTCCTACCTGAGGCTGAGGAAGGAGAAGGGGATGCACTGTTGGGGAGGCAGCTGTAACTCAAAGCCTTAGCCTCTGTTCCCACGAAG
>uc010nxr.1_intron_0_0_1_12228_f| 1:12227-12645
GTAAGTAGTGCTTGTGCTCATCTCCTTGGCTGTGATACGTGGCCGGCCCTCGCTCCAGCAGCTGGACCCCTACCTGCCGTCTGCTGCCATCGGAGCCCAAAGCCGGGCTGTGACTGCTCAGACCAGCCGGCTGGAGGGAGGGGCTCAGCAGGTCTGGCTTTGGCCCTGGGAGAGCAGGTGGAAGATCAGGCAGGCCATCGCTGCCA
CAGAACCCAGTGGATTGGCCTAGGTGGGATCTCTGAGCTCAACAAGCCCTCTCTGGGTGGTAGGTGCAGAGACGGGAGGGGCAGAGCCGCAGGCACAGCCAAGAGGGCTGAAGAAATGGTAGAACGGAGCAGCTGGTGATGTGTGGGCCCACCGGCCCCAGGCTCCTGTCTCCCCCCAGGTGTGTGGTGATGCCAGGCATGCCCTT
CCCCAG
>uc010nxr.1_intron_1_0_1_12698_f| 1:12697-13220
GTGAGTGTCCCCAGTGTTGCAGAGGTGAGAGGAGAGTAGACAGTGAGTGGGAGTGGCGTCGCCCCTAGGGCTCTACGGGGCCGGCGTCTCCTGTCTCCTGGAGAGGCTTCGATGCCCCTCCACACCCTCTTGATCTTCCCTGTGATGTCATCTGGAGCCCTGCTGCTTGCGGTGGCCTATAAAGCCTCCTAGTCTGGCTCCAAGGC
CTGGCAGAGTCTTTCCCAGGGAAAGCTACAAGCAGCAAACAGTCTGCATGGGTCATCCCCTTCACTCCCAGCTCAGAGCCCAGGCCAGGGGCCCCCAAGAAAGGCTCTGGTGGAGAACCTGTGCATGAAGGCTGTCAACCAGTCCATAGGCAAGCCTGGCTGCCTCCAGCTGGGTCGACAGACAGGGGCTGGAGAAGGGGAGAAGA
GGAAAGTGAGGTTGCCTGCCCTGTCTCCTACCTGAGGCTGAGGAAGGAGAAGGGGATGCACTGTTGGGGAGGCAGCTGTAACTCAAAGCCTTAGCCTCTGTTCCCACGAAG
(...)

GFF3 files are now available for the latest NCBI annotation. Here is the link to the human file: ftp://ftp.ncbi.nlm.nih.gov/genomes/H_sapiens/GFF/

and the mouse file: ftp://ftp.ncbi.nlm.nih.gov/genomes/M_musculus/GFF/

If you know the gene name or accession, the UCSC enter link description here can help you, beside the "identifiers" label, open the "paste list ", fill you gene name or accession, and click the " get output" button, select the relate button, you can get an satisfying result.